document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081645>Question 1081645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am having a lot of trouble with Normal Distribution. I do online school and the lessons don't do a very good job of explaining exactly how to solve these problems. My teacher said that all of the following problems were answered incorrectly. Any help is greatly appreciated!!<BR>\n" );
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document.write( "Consider this scenario for questions 5 - 8.\r<BR>\n" );
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document.write( "A standardized test was given to a set of high school juniors and the distribution of the data is bell shaped.  The mean score is 800 and the standard deviation is 120.\r<BR>\n" );
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document.write( "5.  Between which two scores did 95% of the students score?\r<BR>\n" );
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document.write( "z = -1.96\r<BR>\n" );
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document.write( "x = &#956;+&#963;*z\r<BR>\n" );
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document.write( "x = 74+8(-1.96)\r<BR>\n" );
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document.write( "x = 58.32\r<BR>\n" );
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document.write( "z = +1.96\r<BR>\n" );
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document.write( "x = &#956;+&#963;*z\r<BR>\n" );
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document.write( "x = 74+8(1.96)\r<BR>\n" );
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document.write( "x = 89.68\r<BR>\n" );
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document.write( "95% lie between 58 and 90\r<BR>\n" );
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document.write( "6.  To qualify for a special summer camp for accelerated students, a student must score within the top 16% of all scores on the test.  What score must a student make to qualify for summer camp?\r<BR>\n" );
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document.write( "z = +1.96\r<BR>\n" );
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document.write( "x = &#956;+&#963;*z\r<BR>\n" );
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document.write( "x = 74+8(1.96)\r<BR>\n" );
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document.write( "x = 89.68\r<BR>\n" );
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document.write( "90\r<BR>\n" );
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document.write( "7.  What score is 1/2 standard deviation above the mean?\r<BR>\n" );
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document.write( "z = 1/2\r<BR>\n" );
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document.write( "score = 800 + (1/2)120 = 860\r<BR>\n" );
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document.write( "8.  A student scores 900 on the test.  How many more points did the student need to qualify for summer camp?\r<BR>\n" );
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document.write( "5/\r<BR>\n" );
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document.write( "(800 - 240 , 800+240)\r<BR>\n" );
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document.write( "6/\r<BR>\n" );
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document.write( "920\r<BR>\n" );
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document.write( "7/\r<BR>\n" );
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document.write( "800-240\r<BR>\n" );
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document.write( "560\r<BR>\n" );
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document.write( "Consider the following scenario for questions 9-12.\r<BR>\n" );
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document.write( "On the average, members at a local fitness center work out for 90 minutes with a standard deviation of 15 minutes.  The distribution is normal.\r<BR>\n" );
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document.write( "9.  What percentage of the fitness club members work out for 45 minutes or less?\r<BR>\n" );
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document.write( "z(45) = (45-90)/15 = -45/15 = -3\r<BR>\n" );
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document.write( "P(x <= 45) = P(z <= -3) =  (-100,-3)\r<BR>\n" );
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document.write( "0.3%\r<BR>\n" );
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document.write( "10.  What percentage of the fitness club members work out for 2 hours and 15 minutes or more?\r<BR>\n" );
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document.write( "z = (135 - 90)/15\r<BR>\n" );
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document.write( "3%<BR>\n" );
document.write( "11.  68% of the fitness club members work out between which two time intervals?\r<BR>\n" );
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document.write( "P(Z < z) = 0.84\r<BR>\n" );
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document.write( "0.5+0.34\r<BR>\n" );
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document.write( "68% within 1 sd\r<BR>\n" );
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document.write( "between 75 and 105 minutes\r<BR>\n" );
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document.write( "12.  We can say that 99.7% of the fitness club members work out for no more than 135 minutes.\r<BR>\n" );
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document.write( "(Mean - 3 × std) and (Mean + 3 × std)\r<BR>\n" );
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document.write( "(90 - 3 × 15) and (90 + 3 × 15)\r<BR>\n" );
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document.write( "45 – 135 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695704 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695704\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Why would you write <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 74\ +\ 8(-1.96)\"> when you are given that the mean, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \mu\">, is 800 and the standard deviation, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sigma\">, is 120?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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